A307025 - OEIS

%I #10 Feb 16 2025 08:33:55

%S 0,0,0,0,2,56,0,4,374,14980,0,8,2664,302844,19005336,0,12,17556,

%T 6530656,1248702804,278982789260,0,18,121838,151793054

%N Number of (undirected) paths in the m X n knight graph (triangle read by rows with m = 1..n and n = 1..).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>

%F a(1, n) = 0.

%F a(2, n) = (1 - (-1)^n + 2*n*(n - 2))/4 for n > 1.

%F a(n, n) = A288033(n).

%e 0;

%e 0, 0;

%e 0, 2, 56;

%e 0, 4, 374, 14980;

%e 0, 8, 2664, 302844, 19005336;

%e 0, 12, 17556, 6530656, 1248702804, 278982789260;

%e 0, 18, 121838, 151793054, ...;

%Y Cf. A288033 (n X n knight graph).

%K nonn,tabl,more,changed

%O 1,5

%A _Eric W. Weisstein_, Mar 20 2019